Stretched Exponential Fixation in Stochastic Ising Models at Zero Temperature

Abstract

We study a class of continuous time Markov processes, which describes ± 1 spin flip dynamics on the hypercubic latticeℤ d , d≥ 2, with initial spin configurations chosen according to the Bernoulli product measure with density p of spins + 1. During the evolution the spin at each site flips at rate c= 0, or 0 0, q(t) ≤ exp(−t (1/ d ) −ɛ), for large t. In d= 2 we obtain the complementary bound: for arbitrary ɛ > 0, q(t) ≥ exp(−t (1/2) +ɛ), for large t.